Abstract
Non‐native species are among the most important drivers of the structure and function of modern ecosystems. The ecological impacts of a non‐native species ought to depend on the size and characteristics of its population, but the exact nature of this population‐impacts relationship is rarely defined. Both the mathematical form of this relationship (e.g., linear, exponential, and threshold) and the attributes of the invading population (e.g., density, biomass, and body size) that most efficiently describe its impacts could vary greatly across invaders, ecosystems, and ecological variables. Knowing the shape of this relationship could improve management and help to infer mechanisms of interaction between the invader and ecosystem. We used a long‐term data set on the invasion of the Hudson River ecosystem by two species of Dreissena (the zebra mussel, Dreissena polymorpha , and the quagga mussel, Dreissena rostriformis ) to explore the shape of the population‐impacts relationship for selected ecological variables, including seston, phytoplankton, and several taxa of zooplankton. Most population‐impacts relationships appeared to follow a negative exponential form, but we also found apparent thresholds and scatterplots for some variables. Including information on the traits of Dreissena (body size and filtration rate) often substantially improved models of impacts. We found only slight evidence that the resistance of the Hudson River ecosystem to the Dreissena invasion might be increasing over time. Our results suggest important refinements to widely used conceptual models of invasive species impact, and indicate that defining the population‐effects relationship will be essential in understanding and managing the impacts of non‐native species.